Improved Approximation Schemes for Early Work Scheduling on Identical Parallel Machines with a Common Due Date

We study the early work scheduling problem on identical parallel machines in order to maximize the total early work, i.e., the parts of non-preemptive jobs that are executed before a common due date. By preprocessing and constructing an auxiliary instance which has several good properties, for any d...

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Published in:Journal of the Operations Research Society of China (Internet) Vol. 12; no. 2; pp. 341 - 350
Main Author: Li, Wei-Dong
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2024
Springer Nature B.V
Subjects:
Accuracy
Algorithms
Approximation
Employment
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Polynomials
Preempting
Schedules
Scheduling
Workloads
China
90B35
Fully polynomial time approximation scheme
Polynomial time approximation scheme
Scheduling
68M20
Early work
Efficient polynomial time approximation scheme
ISSN:2194-668X, 2194-6698
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Abstract We study the early work scheduling problem on identical parallel machines in order to maximize the total early work, i.e., the parts of non-preemptive jobs that are executed before a common due date. By preprocessing and constructing an auxiliary instance which has several good properties, for any desired accuracy ε , we propose an efficient polynomial time approximation scheme with running time O f ( 1 / ε n ) , where n is the number of jobs and f ( 1 / ε ) is exponential in 1 / ε , and a fully polynomial time approximation scheme with running time O 1 ε 2 m + 1 + n when the number of machines is fixed.
AbstractList We study the early work scheduling problem on identical parallel machines in order to maximize the total early work, i.e., the parts of non-preemptive jobs that are executed before a common due date. By preprocessing and constructing an auxiliary instance which has several good properties, for any desired accuracy ε , we propose an efficient polynomial time approximation scheme with running time O f ( 1 / ε n ) , where n is the number of jobs and f ( 1 / ε ) is exponential in 1 / ε , and a fully polynomial time approximation scheme with running time O 1 ε 2 m + 1 + n when the number of machines is fixed.
We study the early work scheduling problem on identical parallel machines in order to maximize the total early work, i.e., the parts of non-preemptive jobs that are executed before a common due date. By preprocessing and constructing an auxiliary instance which has several good properties, for any desired accuracy ε, we propose an efficient polynomial time approximation scheme with running time Of(1/εn), where n is the number of jobs and f(1/ε) is exponential in 1/ε, and a fully polynomial time approximation scheme with running time O1ε2m+1+n when the number of machines is fixed.
Author Li, Wei-Dong
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  organization: School of Mathematics and Statistics, Yunnan University
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CitedBy_id crossref_primary_10_1109_ACCESS_2022_3225448
crossref_primary_10_1016_j_cie_2022_108386
crossref_primary_10_1007_s40305_023_00511_2
crossref_primary_10_1016_j_cor_2025_107144
crossref_primary_10_3390_computation12040068
crossref_primary_10_1007_s10878_022_00981_9
Cites_doi 10.1016/j.ejor.2020.03.032
10.1016/j.ejor.2019.12.003
10.1016/j.dam.2020.05.023
10.1016/j.cie.2020.106449
10.1007/s10957-017-1147-7
10.1007/s10951-015-0464-7
10.1016/j.omega.2010.06.006
10.1287/moor.8.4.538
ContentType Journal Article
Copyright Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2022
Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2022.
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Issue 2
Keywords 90B35
Fully polynomial time approximation scheme
Polynomial time approximation scheme
Scheduling
68M20
Early work
Efficient polynomial time approximation scheme
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SubjectTerms Accuracy
Algorithms
Approximation
Employment
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Polynomials
Preempting
Schedules
Scheduling
Workloads
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